If they won’t turn on manually, either the switch is burned out or there’s a problem with the wiring or both. You need to get this figured out or pretty much any new switch you put in the same location may have the same problem.
First things first, since some of these are three ways: you are using their add on switch with it, right? And following their wiring diagrams? The GE switches are not wired the same way a dumb switch is for three-way even though they use a physical traveler wire, and the easiest way to burn out the switches is to attach 120 V to the incoming traveler point. 
You got good advice on looking at the zooz As a potential alternative, and they can be used with The existing dumb auxiliary, but the wiring is still a bit different, so you need to follow their wiring diagrams.